7.4 SPM Practice (Short Questions)

Question 4:
A box contains 5 red cards, 3 yellow cards and a number of green cards. A card is picked at random from the box. Given that the probability of picking a yellow card is $\frac{1}{6}$ , find the probability of picking a card that is not green.

Solution:
$\begin{array}{l}\text{P}\left(\text{yellow card}\right)=\frac{n\left(\text{yellow card}\right)}{n\left(S\right)}\\ \frac{1}{6}=\frac{3}{n\left(S\right)}\\ n\left(S\right)=3\times 6\\ =18\\ \\ n\left(\text{not green card}\right)=5+3=8\\ \text{P}\left(\text{not green card}\right)=\frac{8}{18}\\ =\frac{4}{9}\end{array}$

Question 5:
In an office, 300 workers go to work by bus, 60 workers go by car and the rest go by motorcycle. A worker is chosen at random. The probability of choosing a worker who goes to work by bus is ⅔.
Find the probability of choosing a worker who does not go to work by motorcycle.

Solution:
$\begin{array}{l}\text{Let }y\text{ be the number of workers who go to office by motorcycle}\text{.}\\ \text{P}\left(\text{by bus}\right)=\frac{2}{3}\\ \frac{\text{Number of workers }\left(\text{By bus}\right)}{\text{Total number of workers}}=\frac{2}{3}\\ \frac{300}{300+60+y}=\frac{2}{3}\\ 900=720+2y\\ 2y=180\\ y=90\\ \\ \text{Probability}=\frac{300+60}{360+90}\\ =\frac{360}{450}\\ =\frac{4}{5}\end{array}$